class Solution {
public:
    vector<vector<int>> matrixBlockSum(vector<vector<int>>& mat, int k) {
        int m=mat.size(),n=mat[0].size();
        vector<vector<int>>dp (m+1,vector<int>(n+1));
        for(int i=1;i<=m;i++)
            for(int j=1;j<=n;j++)
                dp[i][j]=dp[i-1][j]+dp[i][j-1]-dp[i-1][j-1]+mat[i-1][j-1];

        vector<vector<int>> ret(m,vector<int>(n));
        for(int i=0;i<m;i++)
            for(int j=0;j<n;j++){
                int x1=max(0,i-k)+1,y1=max(0,j-k)+1;
                int x2=min(m-1,i+k)+1,y2=min(n-1,j+k)+1;
                 ret[i][j]=dp[x2][y2]-dp[x1-1][y2]-dp[x2][y1-1]+dp[x1-1][y1-1];
            }
        return ret;

    }
};
